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Formulas in inverse and ill-posed problems /
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Utrecht, The Netherlands :
VSP,
1997.
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| Colección: | Inverse and ill-posed problems series.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Introduction
- 1. Equations and relations in inverse and ill-posed problems
- 1.1 General approach in a theory of multidimensional inverse problems
- 1.2 Control and inverse problems
- 1.3 Generating functions, evolution equations, and inverse problem
- 1.4 Algebraic questions on the theory of multidimensional inverse problems for nonlinear evolution equation
- 1.5 Inverse problem for the Maxwell equation
- 2. Formulas in inverse problems for evolution equations of the general type
- 2.1 Inverse problem. Formal results
- 2.2 Sufficient conditions for correctness of the formulas (2.3), (2.4)2.3 The formulas for solution of the inverse problem in bounded domain
- 2.4 Formulas in the inverse problem for a general evolution equation of the second order
- 2.5 Reduction of multidimensional inverse problems to initial-boundary value problems in Hilbert spaces
- 2.6 Reduction of more common inverse problems to initial-boundary value problems
- 2.7 Formulas in problems of determination of sources
- 3. Formulas in inverse problems for the kinematic problems in seismology
- 3.1 Inverse kinematic problem. Some relations3.2 Formulas for the ray and time
- 3.3 Integro-differential relations and the first integrals
- 3.4 Linear first integral
- 3.5 Quadratic first integral
- 3.6 Generalization of the Herglotz formula
- 3.7 Integro-differential identities in the plane
- 3.8 Determination of the Riemann metric of a special form
- 3.9 The problem associated with an equation for geodesics of the Liouville metric
- 3.10 Determination of a homogeneous functional
- 4. Formulas in integral geometry and tomography
- 4.1 Tomography and inverse problems for kinetic equations4.2 Inversion formulas in integral geometry
- 4.3 An inversion formula in a problem of integral geometry on the sphere
- 4.4 An estimate in a problem of integral geometry
- 4.5 A Radon transformation with variable attenuation
- 4.6 Some relations in tomography
- 4.7 Relations associated with integral geometry
- 4.8 Uniqueness theorems for the inverse problems of kinematic and integral geometry
- 5. The analytical representation of solutions of some inverse and ill-posed problems
- 5.1 Analytical representation solutions of inverse problems for parabolic and kinetic equations5.2 Nonlinear equations and inverse problems
- 5.3 Formulas for solution and coefficients of differential equations of the second order
- 5.4 Formulas for solution of inverse problems for evolution equations in convolution
- 5.5 The operator function method and inverse problems
- 6. Mathematical models in the problems of ethnogeny and evolution of populations
- 6.1 Equations encountered in ecology